Labeled Families in Modular Software Development

We present a general framework for the modular development of families of programs or specifications through the use of labels. Families, consisting of components or versions, appear naturally in software development. The concept of implementation, as an interpretation into a conservative extension, is generalized to labeled families of specifications and formulated in categorical terms. We also show that the category of such families has pushouts and that this construction preserves conservative extensions, as required for composing implementations.